Milnor invariants of braids and welded braids up to homotopy - Université de Picardie Jules Verne
Article Dans Une Revue Algebraic and Geometric Topology Année : 2024

Milnor invariants of braids and welded braids up to homotopy

Résumé

We consider the group of pure welded braids (also known as loop braids) up to (link-)homotopy. The pure welded braid group classically identifies, via the Artin action, with the group of basis -conjugating automorphisms of the free group, also known as the McCool group P dagger n . It has been shown recently that its quotient by the homotopy relation identifies with the group hP dagger n of basis -conjugating automorphisms of the reduced free group. We describe a decomposition of this quotient as an iterated semidirect product which allows us to solve the Andreadakis problem for this group, and to give a presentation by generators and relations. The Andreadakis equality can be understood, in this context, as a statement about Milnor invariants; a discussion of this question for classical braids up to homotopy is also included.
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Dates et versions

hal-04678581 , version 1 (27-08-2024)

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Jacques Darné. Milnor invariants of braids and welded braids up to homotopy. Algebraic and Geometric Topology, 2024, 24 (3), pp.1277-1320. ⟨10.2140/agt.2024.24.1277⟩. ⟨hal-04678581⟩

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